Build on students' informal understanding of sharing and proportionality to develop initial fraction concepts.
Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward.
Van de Walle & Lovin (2006, pp. 67-68) discuss how to help students understand fraction symbols. They suggest making the meaning clear by demonstrating with different configurations of fractional parts and having students count the parts. The teacher then writes the correct fraction name. After at least six examples (same numerator, same denominator, improper), ask the students the following questions:
What does the top number in a fraction tell us?
What does the bottom number in a fraction tell us?
Models for Fractions
Students need experience with all three!
Area - rectangles are better than circles because they are easier to draw and they partition easily
Set - counting number of objects instead of partitioning by size
human fractions
Over time, students should move from the need always to construct or use physical models to carrying the mental image of the model, while still being able to make a model as they learn new concepts or encounter a difficult problem. (Petit, Laird, Marsden, 2010)
To prevent over-reliance
let students become comfortable with model.
Then give them a problem where the model is cumbersome.
Vary the model so students do not over-generalize.
Table of Contents
Van de Walle & Lovin (2006, pp. 67-68) discuss how to help students understand fraction symbols. They suggest making the meaning clear by demonstrating with different configurations of fractional parts and having students count the parts. The teacher then writes the correct fraction name. After at least six examples (same numerator, same denominator, improper), ask the students the following questions:
Models for Fractions
Students need experience with all three!Area - rectangles are better than circles because they are easier to draw and they partition easily
Number line
Set - counting number of objects instead of partitioning by size
Over time, students should move from the need always to construct or use physical models to carrying the mental image of the model, while still being able to make a model as they learn new concepts or encounter a difficult problem. (Petit, Laird, Marsden, 2010)
To prevent over-reliance
Online resources for models
Unit Fractions
Building blocks for all fractions
Every fraction is obtained by combining a sufficient number of unit fractions.
Iterating - repeating a process
K-5 Standards
6-8 Standards
Tape Diagrams